Attractor-Based Coevolving Dot Product Random Graph Model

Abstract

We introduce the attractor-based coevolving dot product random graph model (ABCDPRGM) to analyze time-series network data manifesting polarizing or flocking behavior. Graphs are generated based on latent positions under the random dot product graph regime. We assign group membership to each node. When evolving through time, the latent position of each node will change based on its current position and two attractors, which are defined to be the centers of the latent positions of all of its neighbors who share its group membership or who have different group membership than it. Parameters are assigned to the attractors to quantify the amount of influence that the attractors have on the trajectory of the latent position of each node. We developed estimators for the parameters, demonstrated their consistency, and established convergence rates under specific assumptions. Through the ABCDPRGM, we provided a novel framework for quantifying and understanding the underlying forces influencing the polarizing or flocking behaviors in dynamic network data.